61 or more cards in toolbox decks

[SpencerForHire]

I think the simple fact of the matter is, there is a difference between drawing a mediocre card for your deck and a good card.

It is expected in deck building that some cards are better than others for a given purpose and it is your duty to tune it down to the best 60 "somethings" you can.

[4eak]

Surely you can see that it remains at least possible that some decks exist purely on ratio. Land + Relentless Rats, etc.

Even if there was a way to generate "value" for each card in a deck (a very difficult topic to explore), it still would be possible that certain 61+ card decks would be the optimal.

I don't feel I'm qualified to know the value differences between 61+ and 60 cards (and I doubt you are either to be honest). A silver-bullet toolbox deck is unique enough that it could easily fit into the category of decks which benefit from running more than 60 cards though.

I still think, for now, it's a "60-card myth" which we've simply been taught from our early magic days. For most decks, which have such clear MVP's like Goyf, 60 is obvious. But, decks which have more balanced values between the different cards of a deck are less subject to the 60-card rule.




peace,
4eak

[Rico Suave]

Before addressing specific responses, I challenge anybody in this thread to post a list that is optimal with 61 cards, and I will show you a way to improve it by cutting down to 60.

That's not necessarily true. Especially in decks that aim to cover different situations, the "weakest card" is not always the same.

No it is not always the same, but there IS a weakest card. As such, you should cut it.

Honestly the rigid 60 card limit is more like received wisdom than any actually theoretically solid knowledge. There just isn't enough objective data to make it conclusive. Not to mention many pros do run at least 61 card decks at times. If cutting from 61 to 60 means lower your land count to an unacceptable degree, or cutting a 4-of to a 3-of (which has a much bigger impact on the odds of drawing that card than cutting from 61 to 60 has on drawing any card), then I can see going for a 61 card deck.

There is plenty of data to support it. Have you not seen the math in this very thread? Read Pat Chapin's article, as it has plenty of objective data.

Pros do not run 61 cards. They have in the past, many many years ago, but today? No. Even if you run around and find one list from a recent PT top 8 with 61 cards, I will show you dozens upon dozens of lists that run 60 cards. Just because one pro among 50 might do it doesn't make it right.

If you have trouble with your mana, you can run cards like Ponder which function as something like .3 in regards to your mana count. This is addressed in Chapin's article...

Thats is not true. If the weakest card in matchup A exists, and the weakest card in matchup B exists but the torny will consist of something like 30% deck A and 30% deck B with 40 % other and the card your deciding has similar functions in the other matchups than going to a 61st card is not a terrible idea its simply a minimaly risky one. Silver bullets are awsome when they are relivant, the thing is silver bullets are MUCH MUCH more broken when you have brainstorm and can play something like enlightened tutor with 2-3 tutor targets + counterbalances and tops which you would run anyway.

In survival I would say its boarderline, if the list contains any 4 ofs other than Survival, goyf or mana dorks than its probably better to find another card to cut.

Not every card is a silver bullet. If you are deciding between 2 silver bullets, and can't afford to cut either one, then you need to investigate the other 59 cards because there is always a card that can be cut.

[4eak]

@ Rico Suave

I challenge anybody in this thread to post a list that is optimal with 61 cards, and I will show you a way to improve it by cutting down to 60.

Just how do you think you can "prove it"?

No it is not always the same, but there IS a weakest card. As such, you should cut it.

Before you go off on someone for "not reading the content in this very thread", please recognize the hypothetical situations already presented in this thread which counter your above assumption.

X Mountains and Y Lightning Bolts.dec may actually be optimal at more than 60 cards. (Relentless Rats, whatever)

If you want to argue about optimality outside a vacuum, and inside a specific metagame, the problem becomes so much more complex. Believe me, I would know, I actually try to measure things like this.

Again, you are assuming the above claim. There's plenty of discussion on it, but directly measuring the value of cards is unbelievably difficult to do. I've yet to see such a full mathematical treatment. Genetic algorithms/neural networks for this problem (the easiest solution which isn't biased upon human results and too small a sample size) don't even exist.

Pros do not run 61 cards. They have in the past, many many years ago, but today? No. Even if you run around and find one list from a recent PT top 8 with 61 cards, I will show you dozens upon dozens of lists that run 60 cards. Just because one pro among 50 might do it doesn't make it right.

It doesn't make it wrong either. You should also acknowledge that nobody has said that it would be COMMON for the optimal number to be 61 or more. Even if it is 1 in 50, the point would still be made. There could be exceptions. You have your experience, and some very good reasons to believe that the vast majority of decks are optimal at 60 cards, but you don't proof that there are no exceptions to this rule.





peace,
4eak

[FieryBalrog]

Before addressing specific responses, I challenge anybody in this thread to post a list that is optimal with 61 cards, and I will show you a way to improve it by cutting down to 60.

How do you know it will be an improvement? There's a lot of value-loaded words in this thread that I don't think have earned their keep.

No it is not always the same, but there IS a weakest card. As such, you should cut it.

See above.

There is plenty of data to support it. Have you not seen the math in this very thread? Read Pat Chapin's article, as it has plenty of objective data.

That's not data, or at least its not relevant data. By data I mean objective tournament performances with control groups. You would need to conduct some rigorous tests to determine superiority when even Chapin himself indicates that in a best case scenario, the improvement gained by going from 61 to 60 cards is on the order of 0.07%.

[Illissius]

I still think, for now, it's a "60-card myth" which we've simply been taught from our early magic days. For most decks, which have such clear MVP's like Goyf, 60 is obvious. But, decks which have more balanced values between the different cards

I wouldn't call it the "60-card myth". I'd call it the "60-card rule of thumb". In other words, unless you have a very good reason not to, use 60 cards. One good reason (paraphrased from some article) is that if you really don't know which card to cut and it's the morning of the tournament, you might be better off taking the small but guaranteed hit in consistency from playing a 61 card deck over the chance that you cut the wrong card and do even more harm.

Edit: That said, let me go back to the question of ratios. Land/spell ratio is only one part of the question. Let's say you're playing a control deck, and let's say it has 61 cards in it: 12 draw spells, 12 counterspells, 12 removal spells, 2 win conditions, and 23 lands. What do you cut? The "there is always a worst card" theory doesn't only ignore the variance in card power in the context of different matchups -- which you can explain away with "just average it out over the expected metagame" -- it ignores the variance in the context of different game states. Most of the time, you need a combination of cards which do different things to win a matchup, and furthermore that combination is going to be different in different matchups. Maybe the best card in your deck is Force of Will. So you want the best possible odds of drawing Force of Will. But you sure as hell aren't going to win games if your deck is nothing but Force of Will. To win games, you will need some combination of lands, countermagic, spot removal, mass removal, library manipulation, card draw, and win conditions. And once you break it down like this the change in ratios from adding or removing a card is much more pronounced than just looking at the land-spell ratio, where both are 20+ or 30+ and the difference is so miniscule you maybe can't even fine tune it to the point where you can be sure that the 61 card ratio is better than the 60 card one. So maybe you need at least 3 mass removal spells in your deck to win the midgame against aggro, so you can't cut one of those. And you want at least 6 spot removal spells to reliably survive the early game, so you can't cut any of those either. And you want at least 5 card drawing spells for the late game against the control mirror. And 7 fast counterspells against combo. And you need at least 23 lands. And so on. And once you get down to this level, the difference between 4 and 3 is much greater than the difference between 24 and 23. If you cut one of the cards you "can't cut" to get down to 60, one or more of your matchups is going to suffer. The difference, in perspective, is probably going to be small. But so is the difference in the probability of drawing your best cards between a 60 and a 61 card deck! How can you really say for sure whether the one really small number is bigger than the other really small number?

This is what I mean when I say the 60 card rule is at best a rule of thumb. The idea behind it is compelling, and it's probably going to be right most of the time. But there's all kinds of potential stumbling blocks to the theory which it doesn't even try to address, and the very fact that it's dealing with such miniscule differences makes it very hard to say anything for certain.

[Rico Suave]

[B][SIZE="3"]Before you go off on someone for "not reading the content in this very thread", please recognize the hypothetical situations already presented in this thread which counter your above assumption.

I don't care about hypothetical situations. I care about actual situations that apply to the game we play. As such, I asked someone to post a list that is optimal at 61 cards. So far, there has been nothing of the sort.

Your post is like "well, IF there was a guy who could run the 40 yard dash in 2.2 seconds then this situation would happen in the game of soccer..." but who cares? It doesn't exist.

Does the toolbox deck have 4 Tarmogoyfs and 4 Survival of the Fittest? Then it needs to be 60 cards for best performance.

It doesn't make it wrong either. You should also acknowledge that nobody has said that it would be COMMON for the optimal number to be 61 or more. Even if it is 1 in 50, the point would still be made. There could be exceptions. You have your experience, and some very good reasons to believe that the vast majority of decks are optimal at 60 cards, but you don't proof that there are no exceptions to this rule.

You would make a lot of credit for your argument by providing even just one example of a deck that is optimal at 61 cards. Just one.

Until then, there are no exceptions to this rule.

[Illissius]

Rico_Suave: See, we're coming at this from different directions.

We're saying the theory can't be proven, and we can't be sure it's always true.

You're saying it can't be disproven, at least not until someone shows you a specific example.

The two aren't mutually exclusive.

Edit: And the whole idea that if we show you a 61 card deck you're going to correctly pinpoint the right card to cut is preposterous. I could look up decklists from a Pro Tour, find one that's 61 cards, and paste it here. How could you possibly know what kind of metagame the deck's pilot expected? (And whether that expectation was correct is an entirely different question from whether the deck was correct given the expectation). Have you playtested the deck for weeks so that you know the all of the ins and outs of it and how many of which cards you need when to beat each of the expected matchups? No, you haven't. There's no way you're going to have a better idea of which card to cut than the guy who played it for every single 61 card deck from every single high level event ever.

[4eak]

@ Illissius

Come now, you can finish my quote off...

... of a deck are less subject to the 60-card rule.

I certainly think of it as a 'rule of thumb' in my own deckbuilding. I hope my posts were clear about that. The vast majority of cases, I would suggest a 60-card deck maximum. In fact, I doubt you could find a post of mine which suggests a deck above 60 cards (Minus Battle of Wits.dec). I consider the possibility of an exception pretty rare, although silver-bullet toolbox decks seem the most reasonable place for it to occur.

I called it a myth simply because so many people accept it blindly. You obviously, Illissius, do not accept it blindly.


@ Rico Suave

I don't care about hypothetical situations. I care about actual situations that apply to the game we play. As such, I asked someone to post a list that is optimal at 61 cards. So far, there has been nothing of the sort.

You've not only misunderstood my argument, but you continue to make an outrageous claim that you can optimize 61+ card decks into 60 card decks in all possible cases. You are out of your league. You don't realize you can't even prove your own belief. I could show you a 61 card decklist, and you have no mathematical means to even begin the discussion of the decks optimality or suboptimality, and you have no way to compare the alternatives.

You would make a lot of credit for your argument by providing even just one example of a deck that is optimal at 61 cards. Just one.

Until then, there are no exceptions to this rule.

You would actually have a valid argument if you could say something other than:

I believe X, and since you haven't provided an exception to X, then X must be true.

And, again, it would be nice if you supported your claim that you can optimize any 61+ card deck (which I assume you mean for any format and any metagame as well). Your claim presupposes that you can calculate card value and deck optimality. Please, show me.

My main point is that 61-card decks aren't necessarily suboptimal. We don't have proof for it. The proof is very difficult to produce. Understanding card value and deck optimality is exceedingly difficult. Few here can claim to know beyond a doubt that their deck was truly optimal (even if all of us have said it without thinking).

Testing for the optimality of a single deck type (Burn, for instance) requires atleast millions of games played PER decklist (of which there are many possible decklists) to realistically have a basis for comparison among its variants, even in a vacuum. Playing actual magic against a specific metagame is infeasible to compute for us mortals.

No deck has ever been played enough games (assuming all games were recorded) to say that 'the optimal' build has been reached. You'd be lucky to have 10,000 games with any particular list of cards, and even that is far too small a sample size to see the value discrepancies between a 60 and a 61 card deck or between one card or another.

Here is an example Burn program which might help illustrate how truly small a difference in value we are arguing about. (If you are wondering, yes, I've been working on a robust Burn and Belcher optimizer) Burn is the simplest deck in the game; and for the sake of simplicity, I'm going to argue that we can understand its win-condition status in terms of dealing 20 or more damage.

I set it to "Shock" as the burn spell, and I mulliganed until I had a mountain in hand or only 3 cards left (after brief testing, that appeared to be a decent mull rule). At a million hands per decklist:

Mountain / Shock --- Average Turn on which you Win (Deal 20 damage)
09 / 51 --- 7.9806
10 / 50 --- 7.8711
11 / 49 --- 7.8261
12 / 48 --- 7.8358
13 / 47 --- 7.8832
14 / 46 --- 7.9769

These are really very small differences. Small enough that no human could validly "feel" the difference between the decks in practice. Here's what I got for 1,000 hands:

Mountain / Shock --- Average Turn on which you Win
09 / 51 --- 7.930
10 / 50 --- 7.905
11 / 49 --- 7.839
12 / 48 --- 7.755
13 / 47 --- 7.845
14 / 46 --- 7.962

Before you move on, please compare the numbers. Do you see the problem? From 1,000 hands of testing per decklist, one could assume that 12/48 was the optimal decklist; one could even believe they have "proof" for it. They would be wrong though. Now, I just chose a single set of tests. I'm sure if I run the "1,000 hands" many more times that I could find a set which showcased this issue even more. I don't think I need to though.

You all see how easy it is for humans with even the best anecdotal evidence (that's 7,000 games I just showed you), in as controlled experiment as possible, with no metagame, and least amount of variables to control, etc. would still be quite incapable of proving the optimality of a decklist. You may or may not find optimality by chance with only 1,000 games per decklist (in this case, we didn't). Even if you did find optimality with just 1,000 hands per decklist, that still wouldn't be proof.

Proof is your problem. You can't generate it. Your magic career is largely educated guesswork; so be careful about the claims you make. Do you see why you can't prove to anyone that a 61-card list is truly suboptimal? Even this simple thought experiment is impossible for either of us to prove or know through our own play experience and anecdotal evidence. Imagine how much more complex the discussion of optimality becomes in the context of a wider card pool format, more complex functionality in the tested archetype, the human choice element, flaws in the tournament structure, and the specific metagame in which we wish to play.

A silver-bullet deck, which is practically the opposite of Burn.dec in terms of the ratio of functions (and the variance of each functions value per match) and reliance upon card manipulation, could very well be the deck which breaks the 60-card maximum rule of thumb. Card values in silver-bullet lists have such a huge range, as they are truly metagame defined values. It isn't unreasonable to think that one could produce a metagame in which a silver-bullet deck would prefer the 1-card larger toolbox.

(Just to be clear, this suggests that even huge sets of tournament data is FAR from being proof of optimality; in fact, tournament data is even less reliable with so many variables. You could take every game ever played, and you still wouldn't not know what was the "best deck" or who was the "best player".)



peace,
4eak

[Elfrago]

Without entering in the 61 vs 60 debate, based on my experience, your toolbox should be trimmed to the minimun, because, due to their own nature, the cards in a toolbox shine in one particular situation and suck the others, often being dead draws.
So, revisit your toolbox, I'm sure you will find something to cut.

[Illissius]

Come now, you can finish my quote off...

Sorry, that was just a mispaste. I didn't even notice. I know where you're coming from. I just thought "60-card myth" was a bad choice of words, that's all. (You could call it the "60-cards-are-always-correct-in-each-and-every-situation myth", but that one doesn't roll off the tongue quite so easily.)

[Giles]

A bigger library means a bigger variance in your draws, which is something undesirable.

If we are doing a spell-to-land count and the only thing we care about is if we have a spell or a land. Then it really does not matter how big the deck is. It really is just a Poisson ratio.

Aside:
When magic players dip into the world of statistics, they know nothing. It is not always simple as Thing/Total, and that is true statistic.
What is being dealing with is a binomial probability,expected values, confidence intervals and testing the statistic.

So for the 4eak's brute force method, I would not calculate it like that at all. I would do a binomial probability mass function. Which will give you a better statistic ( Link (note use the pfm to do the test.))
Then I would find the expected value (E(x)=np), then calculate the standard deviation with a sample size larger than 50. Then I would do a Z test to make sure that we are conclusive that it effects something.

[SpencerForHire]

Even if there was a way to generate "value" for each card in a deck (a very difficult topic to explore), it still would be possible that certain 61+ card decks would be the optimal.

This is merely hypothetical conjecture from you, like Rico Suave said you have yet to give an example and I have plenty of 60 card list examples that have won tournaments in every format.

I don't feel I'm qualified to know the value differences between 61+ and 60 cards (and I doubt you are either to be honest). A silver-bullet toolbox deck is unique enough that it could easily fit into the category of decks which benefit from running more than 60 cards though.

I'm much more qualified than you given the fact that I have taken the time to read numerous mathematical threads, articles and even in the past done some napkin math myself to calculate exactly why 60 is better than 61. You are giving reasons why I am wrong based on your own beliefs which are not backed up by any empirical data to prove yourself correct.

I still think, for now, it's a "60-card myth" which we've simply been taught from our early magic days. For most decks, which have such clear MVP's like Goyf, 60 is obvious. But, decks which have more balanced values between the different cards of a deck are less subject to the 60-card rule.

It is the 60 card fact based on the mathematics of consistency. If I wish to see card X in number Y of opening hands I have to run Z copies. The math changes for every card over 60 you play. If your argument is then: "well the percent change between 1 to 2 cards is only a fraction of a point" then you are playing with the consistency level of your deck over all games played. Sure it may not matter in one game, but in every tournament you play where you miss top 8 by one round because you just didn't see that one card you needed, well then you can thank yourself for believing the world is flat because no one ever gave you sufficient evidence to believe otherwise.

Edit: And if your argument is then: the 61st card (which I cut) would have won me that matchup; I would suggest you may need to build a better deck or a better sideboard.

[paK0]

The main problem I have with this thing is that everyone is approaching it very mathematical. You cannot mathematically define the powerlevel of a deck, it's just not possible. The only argument weather a deck is good or not is succes, and since there are hardly any 61-decks out there I think giving the right answear is not really possible.





http://www.starcitygames.com/magic/f...rd_Debate.html

[SpencerForHire]

The main problem I have with this thing is that everyone is approaching it very mathematical. You cannot mathematically define the powerlevel of a deck, it's just not possible. The only argument weather a deck is good or not is succes, and since there are hardly any 61-decks out there I think giving the right answear is not really possible.





http://www.starcitygames.com/magic/f...rd_Debate.html

I disagree. You are looking at this in a very "package deal" way. The power level of a deck has nothing to do with optimization and reduction of randomization as much as possible.

Name any deck of which you may be thinking. Now tell me; if that deck was 0.5% more consistent due to an optimization of a card choice or say, bringing it to 60 cards from 61. Would you rather play that version in a tournament or the 0.5% less consistent version?

[hjalte]

This is merely hypothetical conjecture from you, like Rico Suave said you have yet to give an example and I have plenty of 60 card list examples that have won tournaments in every format.

I'm much more qualified than you given the fact that I have taken the time to read numerous mathematical threads, articles and even in the past done some napkin math myself to calculate exactly why 60 is better than 61. You are giving reasons why I am wrong based on your own beliefs which are not backed up by any empirical data to prove yourself correct.

It is the 60 card fact based on the mathematics of consistency. If I wish to see card X in number Y of opening hands I have to run Z copies. The math changes for every card over 60 you play. If your argument is then: "well the percent change between 1 to 2 cards is only a fraction of a point" then you are playing with the consistency level of your deck over all games played. Sure it may not matter in one game, but in every tournament you play where you miss top 8 by one round because you just didn't see that one card you needed, well then you can thank yourself for believing the world is flat because no one ever gave you sufficient evidence to believe otherwise.

Edit: And if your argument is then: the 61st card (which I cut) would have won me that matchup; I would suggest you may need to build a better deck or a better sideboard.

If you want to do this mathematically, it doesn't matter how many 60-card lists you have, until you have shown, that every single 61-card list, can become more consistent/better, by removing one of the cards.
The problem arises when you, to make a mathematical theory, have to evaluate the power level of every card in the deck. Then you have to take into account the expected/known meta, and compare the cards in your deck, against that meta, and against the overall game plan of the deck. This evaluation of the power level of the cards will certainly be subjective, which will lose you any scientific backup, you wanted to achieve. Even if it wasn't subjective, the problem would be much to complex to model anyway.

So the only way you can possible figure out, if a 60-card list is better than a 61 card list is, if you can obviously point out the weakest card in the list, but that might not be so easy, if you haven't played the deck yourself. Or you can test the hell out of the list, but as 4eak pointed out, it will be close to impossible to test a deck enough to tell, with statistical backup, which card is the weakest.

[paK0]

I disagree. You are looking at this in a very "package deal" way. The power level of a deck has nothing to do with optimization and reduction of randomization as much as possible.

Name any deck of which you may be thinking. Now tell me; if that deck was 0.5% more consistent due to an optimization of a card choice or say, bringing it to 60 cards from 61. Would you rather play that version in a tournament or the 0.5% less consistent version?

If the other version is 0.5% more powerful I might give it a shot. Its a given that we have a shitload of inconsistend Decks running around here. Lets look at Dragon Stompy, it had a time where it was really succesful and a force to be reconed with. However it has always been inconsistent. It trades that for additional power.

Same thing is here, I'm not an expert player nor a math genius, but decks like that or the existence of Dredge with and without LED show me that it can be a good deal to trade consistency for power. And thats what you do by adding the 61st card. Hard to give examples, maybe adding a Relic to a finely tuned Dreadstill list.

Having a greater toolbox is most helpful when you don't know what you will face. If you breakdown a metagame chances are you don't need 61 cards. But if you do not know what to face you can slam the Relic in there, and maybe win just 1 game on the back of it. In the other games you just have to make free two mana and it will cycle. Ill happily trade the 0,5% if I know I get a reasonable shot at winning g1 against any gravebased Deck that might show up.

[Elfrago]

I disagree. You are looking at this in a very "package deal" way. The power level of a deck has nothing to do with optimization and reduction of randomization as much as possible.

Name any deck of which you may be thinking. Now tell me; if that deck was 0.5% more consistent due to an optimization of a card choice or say, bringing it to 60 cards from 61. Would you rather play that version in a tournament or the 0.5% less consistent version?

And lets say that you win all of those 0,5% of matches. Now, the card you're adding MIGHT win you more than 0,5% of matches, and thus running it would still be correct.

[SpencerForHire]

And lets say that you win all of those 0,5% of matches. Now, the card you're adding MIGHT win you more than 0,5% of matches, and thus running it would still be correct.

Then that card should have been in the main over another card. That comes back to optimal deck building.

If the other version is 0.5% more powerful I might give it a shot. Its a given that we have a shitload of inconsistend Decks running around here. Lets look at Dragon Stompy, it had a time where it was really succesful and a force to be reconed with. However it has always been inconsistent. It trades that for additional power.

I would argue that the most powerful factor of a deck is it's consistency.

Same thing is here, I'm not an expert player nor a math genius, but decks like that or the existence of Dredge with and without LED show me that it can be a good deal to trade consistency for power. And thats what you do by adding the 61st card. Hard to give examples, maybe adding a Relic to a finely tuned Dreadstill list.

You won't find any LED Dredge players advocating 61 cards in any large amount. Before you go hit up DeckCheck.net, I am aware there are a few 62 card lists; there will always be outliers.

If you want to do this mathematically, it doesn't matter how many 60-card lists you have, until you have shown, that every single 61-card list, can become more consistent/better, by removing one of the cards.

By that same logic you are failing to find information to prove your point.



Look it comes down to tried and true. Until you can find new data that shows a specific reasoning or technology making 61 cards better, there is no proof. There are countless articles on the subject, all arguments always advocate the math being too minute. If you like playing the odds because your one card is so powerful that it will just win games but doesn't fit into your 60 for god knows what reason then best of luck to you.

[Maveric78f]

I'm writing from a mobile phone, so please forgive me in advance for the short response. I won't elaborate all my statements but I really cannot let this interesting debate without reacting.

First of, Illisius and 4eak made brilliant posts. Maybe the shock/mountain deck is better with a n/61 ratio than with a n'/60 ratio. Just proving so, would demonstrate that 60 cards is not necessarily optimal, even if in practice on a real metagame (not the one restricted to the shock spell). Another argument in favor for 60+ cards is that sometimes, you simply don't know what to cut and the most risk-free choice, given your limited knowledge, is not to cut anything.

Second-of, Nihil is absolutely true about his variance statement. I don't have a clue of what you meant Giles, except maybe: "you all suck at statistics, and I'll prove by claiming something wrong. Most statistic theory are just tools to evaluate (exactly or approximately) complex event probabilities. Basic knowledge can still prove things when it's simple.